g-2 Eigo Shintani (RIKEN-CCS) with Yoshinobu Kuramashi (Tsukuba) - PowerPoint PPT Presentation

Analysis of systematic error in hadronic vacuum polarization contribution to muon g-2 Eigo Shintani (RIKEN-CCS) with Yoshinobu Kuramashi (Tsukuba) and PACS collaboration LATTICE2018, 22-28 July 2018, Kellogg Hotel and Conference Center

Contents Introduction & background 1. Setup 2. Finite volume study 3. Lattice artifact study 4. Summary 5. 2

1. Introduction & background Motivation  HVP contribution to muon g-2 Target precision is < 1% in LQCD Dispersion approach(N f =5) using R-ratio (e+e-) : HLO = 688.6(4.3) × 10 -10 ⇒ 0.6 % precision a m Jegerlehner, 1511.04473 Independent check in LQCD is important. QCD uncertainty is comparable with BNL experimental uncertainty. Will be factor 5 improvement in the new Err[ a m BNL ] = 6.3 × 10 -10 experiment in FNAL, JPARC Need to improve the precision to ~0.5% of HVP muon g-2 in the SM. ⇒ search the new physics in muon g-2 anomaly (~3 σ deviation) 3

1. Introduction & background g-2 with time-slice integral  Time-momentum rep. (TMR) method Bernecker, Meyer, EPL A47(2011)  Vector current correlator <VV>(t) without momentum. Possible uncertainties in both long and short distances • FV effect and t cut truncation error. • Large statistical noise in long distance. • Lattice artifact in short time-slice. 4

1. Introduction & background Our strategy  FV effect  Using the new PACS configs., which are large box size L >10 fm, in the physical pion.  T wo volumes at same cut-off ⇒ direct estimate of FV effect  Statistical noise  Optimized AMA technique in Wilson-clover Mainz, NPB914 (2017)  Volume scaling of S/N ⇒ large volume can reduce noise  Lattice artifact  Comparison with different cut-off.  T est of operator dependence Here we calculate connected HVP contribution only. 5

2. Setup Update  Previous study on 96 4 and 64 4 lattice PACS 1805.04250 Attempt LQCD estimate of • FV. 96 4 lattice:145 MeV pion • 64 4 lattice:135 MeV pion ⇒ chiral extrapolation a m [L=8.1fm] - a m [L=5.4fm] • = (10 ± 26) in 145 MeV LQCD does not disagree • with ChPT, but statistical error is still large. New PACS ensemble, which is L>10 fm in 135 MeV pion. ⇒ direct estimate of FV 6

2. Setup PACS10 configuration  Iwasaki gauge + stout smeared clover fermion  Physical pion mass in N f = 2+1  Old configuration  64 4 , a -1 =2.33 GeV, m p =139 MeV and 135 MeV(reweighted)  New configuration generation (PACS10) PACS, 1807.06237  128 4 , a -1 =2.33 GeV, m p =135 MeV  160 4 , a -1 =3.06 GeV, m p =135 MeV Using PACS10 configs., we can study  Direct estimate of FV effect on L=5.4 fm in m p =135 MeV  Cut-off effect on L>10 fm box in m p =135 MeV All data is still preliminary ! 7

2. Setup Effective mass In t > 1 fm, effective mass of • vector channel is below rho meson mass. free < m v < m r E pp • 8

2. Setup Volume scaling of stat. error • Volume scaling of statistical error • Volume scaling is universal in in long-distance, t > 1.5 fm different cut-off. ⇒ depending on physical volume 9

3. Finite volume study Comparison with 128 4 and 64 4 Integrand, T/a=64 Integrand, T/a=128, extended t m p = 139 MeV m p = 135 MeV (valence) m p = 135 MeV (reweighted) • Backward propagation state significantly affects in T/a=64 from t~2 fm(~T/2) ⇒ check with extended temporal boundary PACS 1805.04250 • LQCD estimate of FV correction is larger than ChPT at t>1.5 fm 10

3. Finite volume study FV effect in L=5.4 fm T -sum, T/a=128, extended t PACS 1805.04250 m p = 139 MeV m p = 135 MeV (valence) m p = 135 MeV (reweighted) Mass correction (4 MeV) agrees with ChPT. LQCD (t cut = 3fm): a m [L=10.8fm] - a m [L=5.4fm] = 40(18), ChPT: 14 ⇒ ~2.5x underestimate 11

3. Finite volume study FV in Strange FV in strange is negligibly small. ⇒ light quark contribution is dominant 12

4. Lattice artifact study Comparison with a -1 =2.33 and 3.06 GeV • Comparison between local- local and local- conserved(point-splitting) current. • Local-local has good scaling rather than local-conserved one at t ~ 1 fm. 13

4. Lattice artifact study Comparison with a -1 =2.33 and 3.06 GeV • Small scaling violation in local-local current even without improvement. • In local-conserved current, one can see 4 — 5 % cut-off effect in ud and s. 14

4. Lattice artifact study LQCD and phenomenology • Compared to R-ratio, LQCD has large value at t < 3fm. • From t ~ 3fm, R-ratio is relatively large, whose integral from t=3-- ∞ gives ~3% contribution in total a m . 15

4. Lattice artifact study a m in LQCD and phenomenology • t cut >2.5 fm, we can see LQCD overshoot phenomenological estimate. • t cut > 3 fm, LQCD is saturated around Exp – a m a m QED+EW+LbL (“no new physics”) 16

4. Lattice artifact study Cut-off effect in a m • Estimate at t cut = 3.5 fm, which may be ~1% truncation error. • Scaling violation is not observed in local-local current beyond statistical error. • LQCD will not favor phenomenological value. • Continuum limit is mandatory, but not yet. 17

4. Summary Outlook  Updated result of FV study in LQCD. PACS 1805.04250  FV study at physical pion  At t cut = 3fm, LQCD estimate is ~2.5x larger than ChPT.  Possible impact to other LQCD estimate of FV based on ChPT.  Lattice artifact study  Compared to two different cut-off  Scaling violation is small even in local-local current on PACS10, while local-conserved has large effect (4 — 5 %).  Next work ud + a m s in LQCD is close to a m Exp – a m  a m QED+EW+LbL (“no new physics”) c + a m  Missing a m disc , but may be <1%, since | a m c | ~ -| a m disc | ~ 1%  Continuum limit is necessary for final result, need one more cut-off. 18

Backup 19

Backup Operator dependence 20